Graphene is of scientific and technical interest because of the extraordinary electronic properties of the two-dimensional material. (Geim, A. K. Science 2009, 324, 1530-1534.) Unfortunately, however, despite its electronic properties, the applicability of graphene in many electronic applications has been limited because graphene does not have a technologically significant band gap>>kT. (Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; and Geim, A. K. Rev. Mod. Phys. 2009, 81, 109-162.) The insufficient band gap limits how strongly the conductance of graphene-based devices can be modulated by extrinsic or field-effect doping—which is a critically important behavior for semiconductor applications.
To address this problem, it has been shown that quantum confinement effects can be used to open up a band gap in graphene. For example, it has been demonstrated that the band gap of graphene nanoribbons, Eg, patterned using electron-beam lithography, roughly varies inversely with the width of the nanoribbons, w, according to Eg˜0.2-1.5 eV-nm/w. (Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. Rev. Mod. Phys. 2009, 81, 109-162; Stampfer, C.; Gutttinger, J.; Hellmueller, S.; Molitor, F.; Ensslin, K.; Ihn, T. Phys. Rev. Lett. 2009, 102, 056403; Yang, L.; and Park, C. H.; Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2007, 99, 186801.) Semiconducting graphene nanoribbons also have been fabricated by “unrolling” or “unzipping” carbon nanotubes.
Unfortunately, semiconducting graphene nanoribbons fabricated using e-beam lithography or by unrolling or unzipping carbon nanotubes have faced challenges in scalability and implementation.